The amount of soil has little influence ; Drainage holes and the nature of the soil are the important factors. Cacti generally need "fast" drainage soil , mostly sand ,gravel, or similar. I have a large "Christmas " cactus that gets covered with blooms. It grew well and was overflowing the pot. I got a larger pot ( with plenty of holes), added potting soil around the edges and planted the cactus without disturbing the root ball. Over several months it deteriorated. I pulled it out of the pot and realized I had made a big mistake to use potting soil because it holds too much moisture. I repotted in sand and gravel and it is now doing very well, although it is about half the size it was before I put it into potting soil.